For centuries, economists have struggled to explain why people and businesses gather in cities.

From an economic standpoint, cities are an enigma. Powerful forces—soaring land prices, intense competition, traffic congestion, overcrowding, pollution—should push people and firms away from urban centers. A business or family seeking a low-cost location will find it in the countryside, not the city's core. "If we postulate only the usual list of economic forces, cities should fly apart," wrote University of Chicago economist Robert Lucas in 1988. "The theory of production contains nothing to hold a city together."

But of course, most people do live in or near cities, and most economic activity takes place in them. In the United States, for instance, 80 percent of the population lives in metropolitan centers that account for just 20 percent of the nation's land area, and they earn nearly 90 percent of the nation's income.

Clearly, cities also exhibit forces of attraction that act with unyielding gravitational power, pulling homes and businesses together. Concentrated markets, economies of scale, sharing of knowledge, access to product variety and cultural amenities have all been suggested as the magnets that draw people toward cities. Like an insatiable vortex, these forces are thought to suck farm kids from homesteads, draw small firms into industry clusters and generate vibrant economies that pull still more people and resources, and feed even greater growth.

The powers of attraction and repulsion are in continuous interplay, centripetal and centrifugal forces constantly in battle, and as economies try to resolve that dynamic tension, cities shift shape and nations transform their internal geographies. Like atoms writ large or microscopic universes, cities vibrate with opposing energies.

Economic tension

A similar creative tension exists among the economists who try to explain cities.* Different schools of thought hold strongly to dissimilar theories about why cities grow as they do. Each school has historic roots; each has modern proponents. And even economists with very similar perspectives on general economic theory often hold quite divergent views on urban growth.

Various Minneapolis Fed economists, for example, differ significantly on this issue, telling tales of two cities and what constitutes their true power of attraction. Prominent theorists like Robert Lucas, an adviser to the Minneapolis Fed, argue that high levels of human capital and knowledge spillovers provide a strong force for "agglomeration," for attracting and stimulating innovators who then become engines of urban growth.

But other leading researchers, including University of Minnesota economist Thomas Holmes, a Minneapolis Fed visiting scholar, suggest that large product markets and low transportation costs have greater explanatory power: Firms and people are attracted to cities because they provide access to markets with low shipping costs.

Another set of economists holds that labor market pooling is the primary explanation for cities. Businesses find it economical to
co-locate where they have access to large numbers of skilled laborers, and workers lower their job search time by being where the companies are located: in cities.

And still other theories suggest that consumption, not production, is the reason cities thrive. Then there are the noneconomic theories: the idea, for example, that politics is what's really behind urban growth—or urban decay.

This is not a mere academic spat. Policy implications are very different. If human capital makes cities grow, government investment in education is a wise policy option. If efficient labor markets are the real cause of city growth, policy initiatives might seek to improve job search programs. If cities grow because people are drawn by bright lights, shopping malls and cultural opportunities, investment in amenities may be advisable.

But the tension shouldn't be overstated. Economists, like the forces they describe, are beginning to find an accommodation that recognizes the contributions of various factors by measuring their empirical strength. Just as cities are constantly trying to resolve their competing tensions, economic scholars are seeking the truth by testing and refining different explanations.

The journey begins by ox cart.

von Thünen's "isolated states"

Two centuries ago, Johann Heinrich von Thünen began developing the first rigorous economic model of a city. His model described "isolated states" and the link between them: urban markets, rural producers and transportation. It was the seed of what would be called, much later, the "new economic geography."

A gentleman farmer himself, von Thünen described an economy in which farmers bringing produce to market in an urban center would incur a transport cost proportional to the distance they traveled. He called these "ox cart costs," since the oxen pulling grain to market would eat some portion of that grain during the trip. (Years later, applying the concept to international trade, Paul Samuelson used the term "iceberg costs"—a fanciful description of a portion of an iceberg melting steadily away as it's towed: the greater the distance, the lesser the iceberg.) A farmer whose land was close to the urban center would benefit from lower ox cart costs but would suffer higher land rents. The pattern, later referred to as a land-price gradient, determined what kinds of goods would be produced near the center and which could still be profitable if grown far from town.

von Thünen's model was very elementary. Modern urban economists—William Alonso, Edwin Mills and Richard Muth—have extended his work significantly. But von Thünen had introduced an essential element for the study of cities and economic growth: the idea of proportional transportation costs and their relationship to overall costs of production.

In addition, von Thünen suggested that while high land rents in cities (and high food prices "on account of the higher cost of transport") militated against their growth, there were a number of forces that might lead industry to concentrate in cities. "[L]arge scale plants are viable only in the capital [city]," he wrote, because the size of a plant "depends on the demand for its products," which is largest in a city. Moreover, he noted, only large plants can profitably install efficient, labor-saving technology, and only large plants work at sufficient scale to use the division of labor. "The labour product per head is far higher in large than in small factories."

Marshall's principles

Alfred Marshall, the British economist, had a different perspective on cities, one that looked less at the costs of farmers bringing products to market and more at the internal dynamics of industry and the cities where they tended to locate. Unlike von Thünen, who wrote at the dawn of Germany's industrial revolution, Marshall had observed decades of England's transformation from an economy based on rural agriculture to one shaped by urban manufacturing.

In 1890, in his classic Principles of Economics, Marshall offered three main reasons that industry and population concentrate in cities:

Human capital and knowledge spillovers "[G]reat are the advantages which people following the same skilled trade get from near neighbourhood to one another. The mysteries of the trade become no mysteries; but are as it were in the air. ... [I]f one man starts a new idea, it is taken up by others and combined with suggestions of their own; and thus it becomes the source of further new ideas."

Input markets
"And presently subsidiary trades grow up in the neighbourhood, supplying it with implements and materials, organizing its traffic, and in many ways conducing to the economy of its material."

Labor market pooling "A localized industry gains a great advantage from the fact that it offers a constant market for skill. ... Employers are apt to resort to any place where they are likely to find a good choice of workers with the special skill which they require; while men seeking employment naturally go to places where there are many employers who need such skills as theirs."

In just a few phrases, Marshall had encapsulated what he saw as the primary forces behind urban growth and geographic concentration of industry. Industries and workers that locate in cities would increase the worker's probability of finding a job and decrease the firm's cost of finding suitable laborers. An industry will create backward linkages, giving birth to nearby input suppliers. And the proximity of skilled workers means that knowledge and skills will transfer among them as if "in the air," generating innovation and new growth.

These were powerful explanations, elegantly stated, and economists ever since have used them as the guiding principles of urban development. Cities, it would seem, are veritable petri dishes for economic activity; they attract pools of willing workers, generate rich flows of ideas and sprout scores of supportive suppliers.

Krugman's geography

But nearly a century later, when economist Paul Krugman, then at the Massachusetts Institute of Technology, began to look at the geography of economic activity, both as it occurred globally and as it evolved within nations, he took another route. Marshall's accounts "surely have considerable validity," he allowed, but "I shall offer a somewhat different approach."

Actually, Krugman's theory does connect to Marshall's idea of input linkages, but it relates more fundamentally to von Thünen's emphasis on transportation costs and his recognition of economies of scale in manufacturing. In a series of papers in the 1980s and 1990s, he develops a model with two sectors, agriculture with constant returns to scale and manufacturing with increasing returns (that is, economies of scale).

In this model, farms can be widely dispersed and of any size since marginal costs won't vary by acreage. But manufacturing will tend to concentrate in large-scale plants at central locations. "Because of economies of scale, production of each manufactured good will take place at only a limited number of sites," writes Krugman. "Other things equal, the preferred sites will be those with relatively large nearby demand, since producing near one's main market minimizes transportation costs." Smaller markets will be served from the central sites. This, say economists, is the "home market effect."

In a circular flow of causation, then, manufacturers will tend to locate near their large markets, and their markets will be large where manufacturers are located. Moreover, Krugman writes, "other things equal, it will be more desirable to live and produce near a concentration of manufacturing production because it will then be less expensive to buy the goods this central place provides." And this relates to Marshall's point about input markets because industries will find low-cost input suppliers in central locations where those suppliers are themselves able to achieve economies of scale—pacemaker manufacturers, for example, are drawn to locate new production facilities in Minneapolis because low-cost suppliers of implantable wire leads have developed there.

Krugman thus explained the forces for centralization of industry and homes in or near large markets. "Cities emerge," he writes, "when manufacturing firms clump together to be near the markets they provide for one another."

Lucas' humans

Like Krugman, Robert Lucas began to study urban growth by first looking at why nations differ so dramatically in their economic growth rates. Lucas, however, focused not on trade and transportation costs, but on how humans enhance their productivity through learning, either in school or on the job—a concept economists call investing in human capital.

Since the early 1960s, economists have looked at human capital as key to differences in individual productivity and earning power. Ph.D.s earn more money than high school dropouts. In fact, U.S. research indicates that in the 1990s an extra year of schooling raised an individual's yearly earnings by between 8 percent and 12 percent.

Lucas concentrated on a different aspect: the external effects of human capital, the productivity spillovers from one person to another. With such externalities, growth in human capital could raise society's overall income even more than it raised the individual's. In his theoretical model these external effects could account for the striking differences in economic growth rates among nations.

But he was also intrigued by the idea that this same effect might explain the growth of cities. "A city is simply a collection of factors of production—capital, people and land—and land is always far cheaper outside cities than inside. Why don't capital and people move outside, combining themselves with cheaper land and thereby increasing profits?" he wrote in 1988. "It seems to me that the 'force' we need to postulate [to] account for the central role of cities in economic life is of exactly the same character as the 'external human capital' I have postulated as a force to account for certain features of aggregate [national] development."

Land rents, he posited, might provide an indirect measure of the force because—as economists since von Thünen have observed—real estate markets must be picking up on something about the relative productivity of land in the center and periphery. "What can people be paying Manhattan or downtown Chicago rents for, if not for being near other people?" asked Lucas. And several years later he developed a rigorous economic model that could employ data on urban land values to measure the size of human capital externalities.

The idea harkens back to Marshall's concept of higher urban productivity because knowledge flows "in the air." As Lucas put it, "we are thinking of course of exchanges of production related ideas ... the probability of useful exchanges increases with the number of people in the area."

Labor market pooling

And then there is Marshall's third explanation: that cities grow because they are efficient labor markets. When workers and employers co-locate, both find it easier to match their needs. Workers looking for a job are more likely to find it where there are lots of companies (that is, in a city). And companies have a better chance of finding the right employee where there are many to choose from (again, in a city).

In 1996, Massachusetts Institute of Technology economist Daron Acemoglu argued that Lucas' approach to human capital and cities was flawed in that it relied exclusively on a "technological" externality—that is, a spillover in which one worker's human capital affected another worker's productivity through the rather mysterious, unmeasurable black box of floating ideas.

Acemoglu, by contrast, developed a model of urban growth through "pecuniary" human capital externalities—spillovers that affect productivity directly through the marketplace—via their impact on the labor market and the price signals provided by wages and job offers. In brief, his work supported the idea that locations with large labor markets—cities—will benefit most from such externalities, buttressing the suggestion that labor market pools, not just knowledge spillovers, account for urban concentration of economic activity.

Putting it to a test

Enough theory. What really happens in cities? What makes them grow? Despite the clarity of explanation, elegance of math and enormity of the literature that surrounds urban growth, these theories have been difficult to verify—or refute—empirically.

Many researchers have measured which industries, cities and locations exhibit higher or lower levels of productivity. But these analyses don't pinpoint the sources of growth. The problem is that all the theoretical sources of economic concentration generate the same kind of productivity; if it all looks alike, there's no way of distinguishing what caused it—observational equivalence, in the jargon of econometrics. "[M]any excellent studies of productivity have told us about the existence of agglomeration economies," write economists Stuart Rosenthal and William Strange in their contribution to the forthcoming volume of the Handbook of Urban and Regional Economics. "They have not, however, had much to say about the sources."

Follow the money

Knowledge spillovers have drawn a great deal of attention from economists, but measuring them has proven difficult. As Krugman has suggested, they leave no paper trail, so most studies have tried to follow them indirectly, through their impact on wages and productivity.

A widely cited 1993 study by James Rauch looked at average education levels and wages across a sample of U.S. cities in 1980 and found that a one-year increase in education was associated with a 3 percent to 5 percent higher wage; housing prices were also higher in cities with more human capital. But whether this truly measures human capital spillovers has been debated; Rauch doesn't account for the fact that people with more income tend to spend some of their money on education—that is, that economic growth may raise levels of human capital, not just the reverse. But in a 2003 paper, Edward Glaeser finds that "reverse causation from growth to education seems to be present only in a handful of declining metropolitan areas."

Another 1993 paper, by Adam Jaffe et al., looked at a more direct "paper trail" of knowledge spillovers by examining geographic patterns of patent citations. The study found that patent citations were five to 10 times more likely to refer to local patents than patents from other cities. This high concentration of invention indicated that, again as Marshall wrote, "if one man starts a new idea ... it becomes the source of further new ideas"—evidently in the same metropolitan statistical area.

In a 1997 paper with Jonathan Eaton, Minneapolis Fed visiting scholar Zvi Eckstein, an economist at Tel Aviv University, followed up on Lucas' 1988 paper with a model in which urban growth is driven by the acquisition of human capital. Looking historically at growth in Japanese and French cities, Eaton and Eckstein showed that increases in human capital could account for historical growth trends in both countries.

More recent work by Glaeser at Harvard, Gerald Carlino et al. at the Richmond Fed and others has also confirmed the existence of external human capital and attempted to gauge its contribution to urban economic growth. But other research casts doubt.

In a 2002 paper, for instance, Enrico Moretti of the University of California, Los Angeles, estimated production functions for manufacturers in a wide range of industries in various U.S. cities and found that "productivity gains from human capital spillovers appear to be empirically relevant." "However," he writes, "the contribution ... to economic growth does not appear to be large ... an average of 0.1% increase in output per year during the 1980s," or about $10,000 a year for the average manufacturing plant.

At the end of an extensive 2003 review of research on human capital externalities in cities, Moretti concludes, "the empirical literature provides some intriguing evidence on [their] existence ... but we are still far from a consensus on the magnitude of such externalities. The empirical literature on the subject is still very young."

Markets matter

Thomas Holmes' work on the geography of economic activity suggests that concentrated markets explain at least as much as human capital spillovers about why cities grow as they do. Indeed, Holmes points out that the Eaton/Eckstein model can be reformulated within an economic geography framework and still match the historical data.

In a 2002 paper, Holmes examines where U.S. manufacturing companies of different sizes locate their sales offices. He points out that while the knowledge spillover theory doesn't argue for any particular pattern of sales office location by size of company, the Krugman theory of concentrated markets suggests that large companies with multiple sales offices will locate them in medium-sized cities so they can serve geographically dispersed markets while minimizing transportation costs of their sales staff. Small firms, which can afford fewer sales offices, will put them in both large and small cities, neglecting medium-sized cities by comparison.

The data confirm that concentrated markets play a significant role. "The estimates indicate that the concentrated-market theory is on the order of half of the explanation," writes Holmes. Knowledge spillovers and other factors explain the rest of the pattern.

How does this relate to why cities form in the first place? "The estimated transportation cost savings of consolidating people into large cities are found to be large in that they outweigh a benefit from dispersion," Holmes explains. "To the extent that the transportation cost factor is of a similar magnitude in other white-collar work, this saving is a force in the formation of cities."

Other efforts

Others have also tried to simultaneously measure the separate contributions of different forces of urban attraction, including labor market pooling.

In a 1997 National Bureau of Economic Research paper, Guy Dumais, Glenn Ellison and Glaeser looked at which industries tend to locate near one another, using relationships among a variety of variables to gauge the relative influence of labor market pooling, knowledge spillovers and input markets. Broadly speaking, their results indicate that labor pools have the strongest impact, followed by knowledge spillovers and then input markets.

Strange and Rosenthal used different techniques to measure the same three forces at several geographic levels: state, county and zip code. "We find evidence of the importance of all of these determinants of agglomeration," they write, but the determinants vary in their spheres of influence. Labor market pools affect economic concentration at all three geographic levels, while input sharing works only at the state level and knowledge spillovers only locally. "Nevertheless, considerable unexplained variation in agglomeration remains," they conclude.

Beyond production

Other research has gone beyond the usual suspects to help explain urban concentration. While most theories have concentrated on how cities thrive because they enhance production, some researchers have also looked at how consumption might be a force behind urban growth. Even Marshall recognized the effect: "[W]e have discussed localization from the point of view of the economy of production. But there is also the convenience of the customer to be considered."

Glaeser, Jed Kolko and Albert Saiz argue in a 2001 paper that cities provide goods, services, amenities, public goods and social interactions not available elsewhere. Museums and theaters are strong predictors of urban growth, for instance.

Along similar lines, Takatoshi Tabuchi and Atsushi Yoshida look at real and nominal wages in a variety of city sizes in a 2000 paper and find evidence in support of consumption effects as well as production effects: While nominal wages are higher in large cities, real wages are lower (with an elasticity between -7 percent and -12 percent), which they interpret to mean that workers are willing to accept lower real wages in large cities because they enjoy the larger city's amenities. As with education, of course, the direction of causality is difficult to confirm: Do cultural amenities promote growth or do healthy economies finance cultural amenities?

Politics undoubtedly plays a role in urban growth, and some have suggested that it's not necessarily a positive one. In "Trade and Circuses," a 1995 article, Alberto Ades and Glaeser argue that while economic factors help to explain cities, politics is more powerful. "Political forces, even more than economic factors, drive urban centralization," they write in their analysis of a cross section of 85 countries and five historical case studies. "Urban giants ultimately stem from the concentration of power in the hands of a small cadre of agents living in the capital. ... Migrants come to the city because of the demand created by the concentration of wealth, the desire to influence the leadership, the transfers given by the leadership to quell local unrest and the safety of the capital."

City of dreams

Debate over the forces that draw people to live and work together will continue as long as there are cities. And history suggests that cities will grow as long as people are able to seek out new possibilities and hope for better prospects. Natural advantage plays a role in urban growth; good infrastructure is essential; markets, labor and education all play a part, however difficult to measure.

But most would agree that human aspiration has long been a central driving force in the formation of cities. It was as far back as 600 B.C., notes urban theorist Jane Jacobs in The Economy of Cities, that the Greek poet Alcaeus wrote,

Not houses finely roofed
nor the stones of walls well built
nor canals nor dockyards
make the city,
but men able to use their opportunity.

*In this article, the term "city" refers to a large agglomeration of population, commerce and culture, including the urban core and surrounding metropolitan areas.

Taking advantage

Location plays a role in determining urban growth, but other factors matter more

At least part of the secret of urban growth lies in three simple words: location, location, location.

Economists call it natural advantage. Historically, cities have prospered when they've been located near natural ports, good soil or mineral deposits. As water transportation, agriculture and mining have declined in economic importance, these advantages have diminished, but other natural advantages still play a role. Silicon Valley didn't prosper because of underground silicon mines, but California's climate may well have allowed high-tech employers there to draw talent that would otherwise have gone to software companies in Massachusetts.

And even when a specific natural advantage loses its ability to attract people and businesses—for instance, when the technology of air conditioning reduced the locational advantage of Northern U.S. cities over Southern cities—cities that prospered because of an initial advantage may maintain an edge because they were "first movers" and built strong economies before others did. Given that head start, first movers can maintain their lead even as their natural advantage fades.

Chicago, for instance, had a very slim window of natural advantage in the 19th century. "Whatever natural advantages the site did have proved transitory," writes Paul Krugman in a 1991 working paper. "Yet once Chicago had become established as a central market, as a focal point for transportation and commerce, its strength fed on itself ... and caused all roads to lead to Chicago."

Recent empirical analyses by economists Glenn Ellison at the Massachusetts Institute of Technology and Edward Glaeser at Harvard suggest that natural advantages might account for about a fifth of the economic concentration that now exists in the United States. But that still leaves 80 percent of the question unanswered.